Apparatus for the practice of celestial navigation



May 2, 1933. R. E. JASPERSON 1,906,752

APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June 11, 1930 1o sheets-sheet 1 ATTORNEY May 2, 1933. R. E. JASPERSON 1,906,752

APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June ll, 1950 lO Sheets-Sheet 2 FIGS n f Ra.. om, T0 N J E VE mf f e m R www ATTORNEY May 2, 1933. R. E, JAsPERsoN 1,906,752

APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June ll, 1930 lO SheeS-Shee 3 `xa ,L

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I ll. 0"5 l Y- f=,f in n man INVENTOR ATTORNEY May 2 1933- R. E. JAsPI-:RSON 1,906,752

APPARATUS FOR THE PRACTICE OF CELES'JIAL NAVIGATION Filed June ll, 1930 10 Sheets-Sheet 4 co n v INVENTOR Rober E-Ja5per5on BY ATTORNEY May `2, 1933.

R. E. JASPERSON APPARATUS FOR THE PRACTCE OF CELESTIAL NAVIGATION Filed June l1, 1930 1o sheets-sheet 5 LOWER LIME CORRECTIONS FOR THE OBSERVED ALTITUDE OF THE MOON UPPER LIMB Obs. AI'. Lower Limb H orzonfal Parallax Obs. AHL

Horzonial ParaIIa x Limb IOS 96 I':l5 198 20,0 2O 20.4 20.7 21,0 2l.

20.5 20B 2I.5 2l. 8

HEIGHT oF EYE CORRECTION Carr-ec Hon Correa Hon IO I2 www FIG. 19

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INVENTOR Rober E- Jasperson Y www@ ATTORNEY May 2, 1933- A R. E. JASPERSON 1,906,752

APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June ll, 1930 10 Sheets-sheet 6 FIG. l1

L- R t@ FIG.14

INVENTOR Rober E.J0sper5on ATTORNEY May 2, 1933. R E. JASPERSON APPARATUS FOR THE PRACTCT-j OF ELESTIAL NAVIGATION June ll, lQO lO Sheets-Sheet 7 Filed ATTORNEY May 2, 1933o R. E. JASPERSON APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June ll, 1930 lO Sheets-Sheet 8 5 0 2 5 l m O INVENTOR Rober E .Jaspers on BY ATTORNEY May 2, 1933. R. E. JASPERsoN 1,906,752

APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June l'l, 1950 10 Sheets-Sheet 9 d' t8 oo 10e 16s a5 2 9 5s 106115164 es 1 e 1Nv1-:NTOR Rober E. Jdsperson BY ATTORNEY May 2, 1933.

E, JAsPERsoN 1,906,752

APPARATUS FOR THE PRACTICE OF CELESTIAL NAVIGATION Filed June l1, 1930 10 SheebS-Sheet 10 FIG.17

CORRECTIONS TO BE. APELIED T0 THE OBSERVED ALTVTUDE OF A STAR OR OF THE SUNS LOWER LIMB, TO FlHD THE 'TRUE Rober E. Jasperson BY MW ATTORNEY Patented May 2, 1933 UNITED STATES ROBERT-E. JASPERSON, 0F MILWAUKEE, WISCONSIN' APPARATUS FOR THE PRACTICE 0F CELESTIAL NAVIGATION Application mea June 11, 1930. `seriai No. 4mes.

(GRANTED UNDER. THE ACT 0F MARCH 3, 1883, AS AMENDED APRIL 30, 1928; 370 0. G. 7 57) This invention relates'to an apparatus for the practice of celestial navigation.

Celestial navigation, that is, the determination of an observers position on the earth by observation of heavenly bodies such as sun, moon, stars and planets, involves in most problems the solution of an astronomical triangle formed by an hour circle through the heavenly body, a vertical circle through the heavenly body, and the hour circle or celestial meridian of the observer. Various so-called short or simplified methods of navigation have been devised, but nevertheless the solution of the astronomical triangle has heretofore required the use of numerous books and tables and considerable calculation with paper and pencil, and the navigator has been required to be familiar with and to know how to apply a group of rules or precepts for particular cases which can not be readily stated in simple definite form, the accuracy of the solution finally depending on the knowledge and skill of the individual navigator and on his ability to perform mathematical operations.

It is well known that mistakes in navigation are due practically entirely to the human element. The navigator, particularly in aeroplanes, must often work under adverse conditions. Rain, wind, darkness, etc. often render it exceedinglyv difficult to handle books, paper and-pencil and plotting instruments with any degree of facllity. When entering involved tables of logarithmic funetions and the like, it is easy to select the wrong value or to transcribe a selected value improperly, and every such entry required multiplies the chances of error. A slight mistake in addition or subtraction may completely negative the result of a computation and require it'to be reworked. A misapplication of rule or precept, such as a mistake in algebraic signs, ruins a computation and once made is difficult to detect. Such errors are easily made under any circumstances and are particularly prone to occur when handling books, paper and pencil in cramped quarters or in wind, rain or darkness, etc., or when working rapidly.

One of the objects of the invention is to definitely stated precepts and by practically eliminating the use of books, paper and pencil and mental calculations.

Another object is to provide a single unitary instrument or apparatus which is small and compact and is adapted for the solution by mechanical means of navigational problems, whereby the solution is made independent of individual mathematical skill and eX- perience.

A further object is to provide navigational apparatus embodying means to provide the necessary data for solving navigational problems and means for solving said problems mechanically without the use of paper and pencil and without mental calculations.

Another object is to provide means for providing tabulated data for the use of the navigator in such a manner that mistakes in selecting the proper value from a table are practically ellminated.

@ther objects will appear more fully hereinafter as the description of the invention proceeds.

`With the above objects in View the invention, broadly stated, resides in the combination in a single unitary instrument of means for providing the data necessary for the solution of navigational problems according to a given method and means for solving the problem mechanically from the data so provided. For the purposes of the present invention as respects said instrument, any suitable method of navigation may be employed. It is preferred, however, to employ a novel method which reduces to simple definite precepts involving a minimum of calculation. This method involves the use of three quantities, A, B and C which may be precomputed and the values tabulated according to values of the latitude L and the local hour angle 2?. From a combination according to definite rules of the quantity A with the declination of any heavenly body, a quantity K is obtained. Then, where he is the computed altitude of the heavenly body above the horizon,

log. csc zc=log. csc K+B (l) A quantity c can now be obtained as followslog. sec c=log. sec K--log sec hc (2) The azimuth Z can then be obtained by a combination according to definite rules of the quantity C and the quantity c.

For a better comprehension of the meaning of these formulae, reference may be had to the dia-gram, Fig. 21. This diagram shows the plane of the observers meridian, PN and Ps being the poles, PNMDPs an hour circle through a heavenly body M, NFBS the plane of the horizon and Z the zenith, ZMF a vertical circle through the heavenly body M, and QDQ the plane of the equator or equinoctial. PNN is equal to the latitude L of the observer, MF is the altitude h of body M above the horizon, MD is the declination d of the body M, the angle NZF is the azimuth of body N, and angle ZPNB is the hour angle t. It Will be seen that PNBN and MBF are two similar right spherical triangles and from Napiers rules cot PB=cot L. cos t (a) cos PBN2cos L. sin t 15) tan NB=sin L. tan t (c) The side MB of the smaller triangle, which is the quantity K referred to above, may be expressed as a combination of (PB 90) +d. Again applying Napiers rui-es, and using k for side LIF- Sin h=sn K. sin PEN (al) DSoos K cos Fa -COS h (e) Azimuth=NBFB (f) The quantity (PB-90) is the quantity A above referred to, and cot PB=tan (PB- 90) =tan A, Equation (a) may now be written tan --cot L. cos t (a) The quantity B above referred .to is the logarithmic cosecant of angle PBN which may be found from Equation (b) The quantity C above referred to is the side NB which 'may be found from Equation (c). Each of Equations (a), (o), and (c) depends for its solution on L and t, and henne A, B and C may be precomputed and tabulated for values of L and t.

Equation (d) may now be written as above log csc z=log csc K-l-Z? (1) log sec c=log see Xlog see Azimuth,

As will be understood by those skilled in the art, the computed altitude of the heavenly body and its azimuth are all that is required for working a line of position. Apparatus embodying the invention, as adapted to this method of solution, must provide precomputed values of A, B and C for given values of latitude and local hour angle, and values of log cosecants and log secants, together with a suitable means for solving the above Equations (l), (2) and (3). The invention as illustrated in the drawings and as described hereinafter embodies the above features, but it is to be expressly understood that the dra'Wing's are for purposes of illustration only and that apparatus embodying the invention is capable of adaptation to other methods of navigation as Well as other mechanical forms, reference being had to the appended claims for a definition of the limits of the invention.

In said drawings- Fig. 1 is a plm view of an apparatus e1nbodying invention;

FigV 2 is a partial end view of 1;

Fi 3 is a sectional view taken on the line E of Figo 4;

fris a sectional view teiten en the iine AWA Fig. 3;

Fig` 5 is a sectional view en the line B-B of F ig1 3;

Figa 6 is a sectional view on the line C-C of Fig. 1;

Fig. 7 is a sectional view on the line D-D of F ig. 1;

Figs. 8 and and a sectie ai 1 and associated La 1;

Figs. 10 and aw respectively a sectional view and a side view of an operating Lively an end view i operating shaft knob;

Figs. i views of index devices li g glasses;

Figs. 14 to i les employed in the use oi `the appav 14 showing in section the preferred construction of tabes to be enihodied in the machine;

F 18 an 19 shot? tables employed in correcting sextant aititudes and are shown for purposes of explanation of examples of navigational problem.;l explained hereafter;

Fig. 2G is a plan viev.r of a plate mounted on the apparatus; and

1 Fig. 21 is a diagram illustrating the derivation of formulae in the preferred method explained above.

In the form shown, the principal data required is preferably embodied in the apparatus in the forni of tables on sheets or tapes movable past suiteoie indices or reading de vices in any si le manner.V The data from these tabl in the form of simple numerical quantities, may be used in formulee 1, 2 and 3 above, which involve only addition and subtraction, so that the computing or calculating mechanism .generally speaking need only be capable of performing addition or subtraction to complete the desired solution.

The apparatus is housed in a casing 1 of yany suitable type that is preferably provided with glass sides 2 held in place by any suitable means such as clips 3 secured to the casing. The upper part of the casing houses a suitable computing or calculating mechanism capable of adding and subtracting which as shown comprises six vertical rows 4 of keys from 1 to 9 inclusive, avertical row 5 of keys from 1 to 5 inclusive, a vertical row 6 ofv keys from 1 to 9 inclusive, and a vertical row 7 of keys from .1 to .9 inclusive. The vertical rows 4 add or subtract numbers as large as six figures, the rows 5 and 6 provide for sixtieth fractions of numbers, and the row 7 provides for tenths of siXtieth fractions. The rows 5, 6 and 7 are desirable for working with time or arc wherein the hour or degree respectively is divided into sixty minutes, and if greater accuracy is desired, additional rows of keys may be added. Numbers set on the keys of the apparatus may be registered in the apparatus and printed on a suitable tape 8 by pullingl the operating handle 9. Addition or subtraction will be performed by the apparatus by depressing the proper key 10 or 11 and pulling handle 9, and the resulting addition or subtraction appears printed on the tape 8 and is preferably marked as a step performed by the machine by a printed asterisk or the like. The mechanism is preferably also adapted to print the words away or toward by depressing the proper key 12 or 13 respectively, and four keys 14 provide for printing the letters N. S, E or W. Preferably the apparatus is adapted to leave a space on the tape between a figure printed by a key in the right-hand row 4 and a figure printed by a key in row 5 and to print a dash-in this space whenever a key in row 5 is used. The mechanism may also be cleared in any suitable manner, as by pulling handle 9 twice without depressing key 10 or key 11. The adding and subtracting mechanism within the housing 1 may be of any suitable type, machines of this character being well known, andthe specific form of said mechanism forms no part of the present invention.

The tables to be embodied in thc apparatus, as shown in Fig. 14, preferably comprise a sheet or strip of paper or the like 15 on which the tabulated values are printed, said sheet or strip being mounted on a flexible back 16 of any suitable material such as linen. Fig. 15 shows the preferred form of one of the principal tables required, which is hereinafter referred to as Table I and gives values of A, B and C, the entering arguments being the latitude L and the local hour angle t. As shown in Fig. 15, these data are arranged in a series of main columns, each main column containing live sub-columns or rows of gures. The two left hand rows 17 and 18 of each main column contain the values of latitude L and local hour angle t respectively, while the other three rows 19, 20 and 21 contain values of A, B and C respectively. In the left hand row 17, the latitude begins with zero degrees at the top and reads down to ten degrees at the bottom, the increment between successive values being preferably 30. For each such value of latitude, values of hour angle t are given in row 18 in degrees from zero to ninety degrees, the increment between successive values of t being 30 of arc. ln the second main column, the rows 17 to 21 inclusive begin at the bottom and read upwardly as clearly shown in Fig. 15, so that consecutive values of latitude and hour angle may be read down one main column and up the next, etc.

This table is preferably arranged on suitable rollers or the like whereby it may be moved past a window 22 in the casing 1, the values being read through a glass 23 sliding on guides 24. Referring to Fig. 12, glass is preferably provided with vertical lines forming rows or columns corresponding to the sub-columns 17 to 21 of Table I, the spacing of these lines on the glass corresponding with the spacing of the lines separating said sub-columns on Table I. Between tlie lines on the reading glass are preferably the letters L, t, A, B, and C corresponding to the headings of rows 17 to 21 on Table l, while at the bottom of the glass 23 appear' the letters L and Z in the two left hand colunms for a purpose to be described hereinafter. Tt will be seen that owing to the spacing of the lines separating the columns, the reading glass can be set only in 011e position on the guides 24 for each main column of the table in which the sub-columns will correspond properly, and this column may be selected readily by the latitude headings shown in Fig. 1 that are placed on the casing 1 adjacent the edges of window 22. lf the navigator is working in a latitude between 21 degrees and 31 degrees, the proper maln column is quickly selected by means of these figures and the reading glass set in position as shown in Fig. 1, and in this position the, lines on the reading glass correspond to the lines separating the sub-columns in the table.

In the form shown, Table I passes over a guide roller 25 rotatably supported in brackets 26 immediately below the window 22 and is attached at its ends to two spools 2T by any suitable means such as battens 28. .Spools 27 may be rotatably supported in any suitable manner, as by means of brackets 29 on the opposite sides of the casing.

Suitable means are provided for rotating either of the spools 27 to wind up Table I thereon, the other spool 27 being free to rotate, and preferably each of the spools can be driven only in a direction to wind up Table I thereon in order to prevent unrolling and loosening of the table. In the form shown, an operating shaft 30 carries on its inner end a gear 31 that is axially movable to engage either one of a pair of gears 32 one on each of the spools 27 (Fig. 4) Gear 31 is loose on shaft 30 and housed wiihin the gear (Figs. 8 and 9) is a ratchet wheel 33 secured to said shaft and a pawl 34 secured to the gear and pressed into engagement with the ratchet wheel by a spring 35. Shaft 30 will therefore drive gear 31 in one direction only, that is, counter-clockwise as seen in Fig. 8, or clockwise as seen in Fig. 3, so 'that the upper gear 32 can be driven only in a counterclockwise direction and the lower gear in a counter-clockwise direction as viewed in Fig. 3.

Preferably locking means are likewise pro-S vided so that when gear 31 is moved axially to engage one of the gears 32, it remains in that retaticn of knol is position and can be moved to engage the other of gears 32 only by resetting the locking means. When the latitude is increasing, for example, and the apparatus is set to move Table I 'in the direction in which the latitude vaues appearing under window 22 increase, the apparatus remains set in this position and at any time that it is used the navigator can move the table only in the proper direction. In the form shown, shaft 30 is longitudinally slidable in bushing 36 that is rotatably mounted in the brackets 29, a spring 37 being interposed between the bushing and gear 31. An operating knob 38 having a recessed head through which shaft 3() passes is threaded on the outer end of bushing 36 and held in place by suitable means such as a set screw 39. The outer end of shaft 30 is provided with a head 40 on which is formed a laterally extendirf" lu" 41 adapted to engage notches 42 43 ormed in the operating knob 38. As .shown in Figs. 10 and 11, notch 42 is shallow, while notch 43 is rela` tively deep. VVhefA the lug 41 engages notch 42, shaft 30 can be displaced inwardly only to the position shrwn Fig. 4 wherein gear 31 engages the lower 32, and Table I can be moved iii one di; ation only since the Ative in one direce.- tion only by v le of the ratchet and pawl 33, 34. TWhen it i* esired to move the table in the opposit l rec-tion, head 40 is pulled outwardly and 4 ngaged from notch 42, whereupon s rota ed to engage lug 41 with note i so that shaft may be displaced inward* iiicientl;7 to engage gear 31 with the upp l Rotation of knob 38 in its eective direction now moves the table in the opposite directies. is

seen that knob 38 is always rotated in the same direction, and the direction of movement of the table is controlled by the engagement of lug 41 in notches 42 or 43 so that the table always moves in the same direction unless the locking means is reset.

Fig. 16 shows the preferred form of the second principal table required, which will be hereinafter termed Table II. Each main column of Table II is divided into seven subcolumns or rows. In the two left-hand rows 44 of each main column are tabulated degrees and minutes, reading from the top down, and in the two right-liand rows 45 of each main colunin are tabulated degrees and minutes reading from the bottom up. Between these rows in rows 46 are values of log cosecants and log secants, and as will be clear from Fig. 16, the values of these functions may be obtained from the table for any angle between zero and ninety degrees, reading from the top down for zero to forty-five degrecs and from the bottom up for forty-live degrees to ninety degrees. seventh column 47 headed d may be added giving the tabular differences for purposes of interpolation.

Table II having been madeiip is preferably reduced in size photographically and mounted on the periphery of a drum 48 rotatab'y mounted by means of axles 49 in the brackets 29 and provided at one side of the casing with an operating knob 50. Preferably a shield 51 covers the upper portion of drum 48, said shield being provided with an opening 52 in line with a window 53 in the casing 1. Table II is preferably viewed through a magnifying reading glass 54 slidably mounted on suitable guides 55 adjacent the window 53. As seen in Fig. 13, reading glass 54 is provided with lines corresponding to the ines separating the seven sub-columns of each main column of Table II, so that the setting of the reading glass will correspond with the main columns of Table II in one position only for each column. Preferably, reading glass 54 is provided with headings corresponding with the headings of T able II, and the desired main co'umn of Table II may be readily selected by reference to the indications adjacent window 53 on the casing giving the limiting numbers of degrees in each main column and also the limiting va`ues of log cosecants and log secants in each main column. If values between fifteen and twenty degrees, or between seventy and seventy-five degrees, are desired, the glass 54 is quickly shifted to the position shown in Fig. 1 wherein the lines of the reading glass correspond with the lines of the main column of Table II. Preferably the width of slot 52 is sufiicient to uncover two adjacent tablilar vaues for purposes of interpolation.

Preferably an instruction plate 56 is mounted on the casing 1 between windows 22 and 53, said plate as more particularly in Fig. 20 bearing precepts and formul for the use of the apparatus.

Fig. 17 shows a conversion table for converting from hours and minutes of time to degrees and minutes of arc that is preferably also mounted on drum 48 and is hereafter referred to as Table III. In addition to the above data, a copy ofThe American Nautical Almanac, an annual publication by the United States Naval Observatory, will be required for the solution of problems.

Figs. 18 and 19 illustrate portions of welllmown tables of corrections which must be applied to seXtant readings to obtain the trueobserved altitude of a heavenly body above the horizon. These tables do not require more than three pages of ordinary size, and while they may be supplied with the apparatus in a manner similar to Tables I, II and III, they may preferably be embodied in the Nautical Almanac together with logarithmic tables from 100 to 999. vThe Nautical Almanac, which varies from year to year is preferably separate from the apparatus. Figs. 18 and 19 are shown herein in the interest of clearness of the following examples of actual solutions.

In the following illustrations of typical problems and their solutions by the use of the present invention, the right hand column of figures represents the printed record that would appear on tape 8. The symbols and explanatory remarks to the left of these iigures indicate the sources of values obtained and steps performed. The following symbols and abbreviations are employed A, B, C,-tabulated functions of Table I K, c-functions computed by formulae 1 and 2 W,-watch time CW,-diference between chronometer and watch time C. F.,-reading of chronometer face with 12 hours added in some cases) C. C.,-chronometer correction G. C. T.,-Greenwich civil time Eq. T.,-equation of time G. A. T.,-Greenwich apparent time D. R.,-dead reckoning L. A. T.,-local apparent time 15,-hour angle fZ,-declination hc,-computed altitude LS,-sextant altitude L,-true altitude L. S. T.-local sidereal time It. A.,-right ascension Z,-azimuth A plane enroute from Pensacola, Fla., to Fayal, Azores Islands, at about 8.00 A. M. on July 27, 1930, is in dead reckoning position, Lat.=e0O N., Longn=70o W., course 70o true, speed 80 knots. Height of eye 200 ft. From a previous comparison of the navigators Watch with the chronometer, 6' `W= 4h 08In 36S, the chronometer being 3m slow at the last radio time signal. The navigator glitained 7a sextant altitude of the sun h.'=

Correct1on (Fig. 18, Table B) 8.1

Additional correction (Fig. 18) .2

The navigator now sets the index glass 23 to the main column of Table I containing values of latitude from 21 to 31 and turns knob 38 until the values L=30, t=69 appear in the window 22, and at the same time the values A==3149.7, B=23026, and 0:12795. Referring to instruction plate 56, the navigator notes that when latitude and declination are both north (same name), then K=d+A and azimuth Z=Ca. The solution is then completed by the apparatus as follows d 19-19.8N A S31-49.7 K (=dl-A) {i1-09.5* B 23026-000 Log csc K 10853-000 Log csc he 33879-000* Log sec K 20262-000 Log sec kc 5121-000 Log sec o 15141-000 it, 27-16.9 27-06.9 Altitude difference 10.0' away C 127-30.0 c 45-06.0 Z 82--24.0*N-E .(Note: The above computation requires l three settings of index glass 54, one to obtain log sec. and csc of K, one to obtain he and log sec. he and one to obtain 0. These settings are readily made by virtueof the delimiting values on the casing.)

The navigator plotted this line of osition and obtained a new position whic he assumes to be his best position at 8.00 A. M., as follows:

The next problem for the navigator is to determine the interval to noon and to find the watch time and Greenwich civil time of transit. The value of t at the time of the morning sight was 69 which from Table III is l4:"-36m and is the time required for the sun to reach the observers meridian if he remained stationary. The navigator determines from his chart that on course true, speed 80 knots, he is flying eastward or toward the sun at the rate of o-longitude per hour. The rate of travel of the sun is 900 per hour. Using ordinary logarithm tables, which as above stated are preferably embodied in the Nautical Almanac, the navigator solves the formula; interval to he will be in dead reckoning position- Lat.=31-53-24 N. Y Long.=64-22-06 W. The navigator now computes the altitude of the sun on the meridian. In this case t=0, A=90Lat., B=0, and C=180. The solutionv is therefore greatly simplified 90-00-0 Lat 31-53.4N.

A 58-06.6* d (Nautical Almanac) 19-17.4N. K (=a+A) 77 24.o*

Since 13:0, K=tc or the altitude of the sun for the assumed position. At the time of transit, the navigator obtains a sextant altitude of the sun which, corrected as explained above for the morning sight, is 77-44 l.0.

` 20.0* toward K being less than 90, C being 180, and c being v0 (since k and K are the same), the navigator knows that the azimuth of the sun is 180 (bearing south). The altitude difterence being toward the sun, the D. R. latitude is corrected as follows:

D. R. Lat.: 5510-53-24 N.

dia-2e' s.

Noon Lat. 31-33-'-24 N.

The 8.00 A. M. position line is then transferred on the navigators chart to intersect the new latitude line to obtain the noon lix.

Shortly after sunset, about 7.15 P. M. that evening, the navigator observed an unknown star bearing 52 true and obtained a sextant altitude of 31-30.2. His dead reckoning latitude at the time was 30 N. From instruction plate 56, the navigator knows that when Z is less than 90, K=L+A- lSolving for d and t and entering Table I with L: 30 and Z=52 (bottom headings of index From local sidereal time, previously determined to be 3h-56m-56".6, and hour angle t, the navigator determines the right ascension of the star as follows:

Entering tables of apparent places of stars in the Nautical Almanac with right ascension and hour angle as arguments, the star is found to be Deneb (a Cygni). The line of position of Deneb can now be worked in the same manner as the line of position for the sun as explained above.

The above examples are typical of the solution of problems encountered by the navigator in both surface and aerial navigation during the course of a days work and it will be seen that the invention provides a simple, compact and unitary instrument whereby errors due to the human element are avoided. In aerial navi ation over lar e bodies of water or over un amiliar land te high speed at which planes travel combined with winds of uncertain force and direction render it imperative that a navigator or pilot check his position continuously by observation of heavenly bodies. Consider, for instance, a pilot flying alone over a considerable stretch of Water. He is occupied primarily with staying aloft and While so occupied has little time to devote to laborious computations, but still he must know with reasonable accuracy what his position is and how it varies due to forces beyond his control. U

The present invention relieves the navigator or pilot of practicall all of the mental efl'ort of solving his pro leins. All 'books have been eliminated with the exception of the Nautical Almanac and until the data contained in the latter are compiled in some better form, the pilot can obviate the necessity foi turning pages in the Almanac by securing the few pages that he expects to use on a cardboard folder, board, etc. The same folder or board can be employed to hold the tables for correcting sextant altitudes shown in Figs. 18 and 19.

The two principal tables required to solve problems in line of position or star identiication, together with the table for converting from time into are, are all emboded in the apparatus, together With complete iiistructions 'or precepts appearing on the face of the instrument Where they are readily available. The Work of solving a given problem may be done with one hand, with no mental calculation, and with an assurance that the results are correct which does `not obtain Where the navigator is working with pencil and paper, unless each problem is cai-efully checked over for possible arithmetical errors. The accuracy of the results obtained is as close as with any other method employing live place logarithms.

An error frequently arising in using tables in book form is that Which results from picking out the Wrong quantity, either by selecting the Wrong quantity in a proper co1- umn, or by taking the quantity from the Wrong column, etc. When an entire page is in view at once, such errors are easily made, particularly1 when the navigator must hold the book open at the proper page and hold a finger or pencil at the proper value with one hand While Writing down the value with the other. Errors of this kind are el'minatcd with the present invention because the index glass deliinits the proper column ywhile the Window deliinits the proper line in that column. Adjustment of the index glasses to the proper column and of the operating knob may be made with one hand and the apparatus Will remain 'set While the navigator uses the same hand if desired to set the value on the computing mech anisni.- p

Each step is printed on the tape 8 as it is performed, so that the navigator can tell at a glance that herphas employed the intended quantity. Moreover, a permanent printed record is provided, and as each problem is completed, it may be labeled and retained giition now in use still rely on the use of tables in book form and pencil and paper calculations. The use of diagrams of various types has likewise been suggested, but these are subject to as great if not greater chances of error as the commonly used method. Geometrical instruments lack accuracy and ai'e cumbersome and unwieldly and hence diflicult to handle. The present invention provides a means for solving navigational problems as accurately as any practically used method, a means which is unitary and selfcontained, constituting a single, small, compact instrument, and a means which eliminates books, tables in book form, and mental calculations whereby the accuracy of the solution is made substantially independent of the abilityof the individual to perform arithinetical steps.

It will be understood that the invention is not limited tothe embodiment described and illustrated in the drawings. For example, apparatus embodying the invention may be adapted to other methods of solution of navigational problems involving other formulae and other tabulated values. Moreover, the mechanical details of the apparatus described and `illustrated may be varied without departing from the spirit of the invention.

Thus, the tabular data may be embodied in the apparatus in other foiins than that shown, other types or ,arrangement of computing mechanism maybe employed, and changes may be made in the form. details of construction, and arrangement of the mechanical features, all Without departing from the spirit of the invention. Reference is therefore to be had to the appended claims for a definition of the limits of the invention.

The invention herein described mav be used by or for the Government of the United States of America for governmental purposes Without the payment to nie of any royalty thereon or therefor.

What is claimed is:

1. Apparatus for the solution of navigational problems comprising the combination in a unitary self-contained instrument of means embodying tables of functions of an astronomical triangle, index means for selecting desired values from said tables, means for presenting said tabulated values in succession to said index means, and mechanical means for performing addition and subtraction, said tables comprising values precomputed and combined into functions necessary for the desired solution by said niechanical means and said mechanical means having operating members corresponding to values selected from said tables.

2. A unitary self-contained instrument for solving navigational problems involving the solution of an astronomical triangle comprising a casing, means in said casing embodying in tabulated lform values of functions of an astronomical triangle, index means for delimiting and selecting a particular value from said first named means, means in said casing for moving said first named means to cause said values to pass in succession past said index means, and adding and subtracting mechanism in said casing and co-related with said first named means for combining indexed values into a value designating a solution of an astronomical triangle, said tabulated means comprising values precomputed and combined into functions necessary for the desired solution by said mechanism and said mechanism having operating members corresponding to Values selected from said tabulated means.

3. Navigational apparatus for solving an astronomical triangle comprising the combination of means embodying values of functions of an astronomical triangle necessary to the desired solution, index' means for selecting a particular value, manually operable means for presenting said values in succession to said index means, and mechanical computing means co-related with said first named means to combine indexed values of said functions, said computing means bearing indicia corresponding to said tabulated values.

4. A navigational instrument com rising in combination means embodying va ues of functions necessary to the solution of an astronomical triangle, a casing, said means being movably mounted in said casing, index means for delimiting and selecting a particular value, means for moving said first named means to present said values in suecession to said index means, and mechanical computing mechanism mounted in said casmg and co-related with said first named means to combine indexed values of said functions, said computing mechanism having operating members corresponding to values selected by said index means.

5. A navigational instrument comprising in combination a casing, means movably mounted in said casing and embodying values of functions necessary to a solution of navigational problems, means including a manually operable member and effective in one direction of movement only to move said first named means, means for selecting desired values, and computing mechanism in said casing for combining selected values of said functions, said computing mechanism bearing indicia corresponding to said values.

6. A navigational instrument comprising in combination a casing, means movably mounted in said casing and embodying values of functions necessary to a solution of a navigation problem, a manually rotatable member, operating connections between said lnember and means and effective in only one direction of rotation of said member to move said means, index means for selecting desired values of said function, and computing mechanism in said casing for combining indexed values of said functions, said computing mechanism bearing indicia corresponding to said values.

7. A navigational instrument comprising in combination a casing having a window thereim means mounted in said casing for movement past said window and embodying values of functions necessary to a solution of a navigational problem, a manually operable member for moving said means, and computing mechanism in said casing for combining values selected through said window into a Value designating a solution of a navigational problem, said mechanism having operating members bearing indicia corresponding to said values.

8. A navigational instrument comprising in combination a casing having a window therein, means mounted in said casing for movement past said window and embodying values of functions necessary to a solution of an astronomical triangle, a manually operable member for moving said means, an index means slidable along said window to select desired values appearing therein, and computing mechanism in said easing corelated with said first named means for combining indexed values, said computing mechanism having operating members bearing indicia corresponding to said values.

9. Apparatus of the class described comprising in combination a casing having a Window therein, means movably mounted in said casing for movement past said Window and embodying values of functions necessary to a solution of navigational problems, a manually rotatable member, operative connections between said member and means and effective in only one direction of rotation of said member to move said means, index means movable along saidowindow to select desired values appearing therein, and computing mechanism in said casing and co- Vrelated with said first named means for combining indexed values of said functions, said computing mechanism having operating members bearing indicia corresponding to said values.

10. Apparatus of the class described comprising in combination a casing having a pair of Windows therein, a plurality of means movably mounted in said casing for movement past said Window and each embodying values of functions necessary to a solution of navigational problems, manually operable means for moving each of said first named means independently, index means for each of said Windows for selecting desired values appearing therein, and computing mechanism in said casing and co-related with said first named means for combining indexed values of said functions into a value designating the solution of a navigational problem, said computing mechanism bearing indicia corresponding to said indexed values.

11. In apparatus of the class described, the combination in a single instrument of a casing having a Window therein, a rotatable means in said casing embodying in tabulated form values of functions necessary to a solution of navigational problems, manually operable means for rotating said rotatable means past said Window, an index slidable along said Window for selecting desired values appearing therein, and computing mechanism in said casing and co-related with said rotatable means for combining indexed values of said function, said computing mechanism bearing indicia corresponding to said indexed values.

12. In apparatus of the class described, the combination in a single instrument of a casing having a Window therein, a rotatable means in said casing embodying in tabulated form values of a plurality of functions necessary to a solution of navigational problems, the individual functions being arranged in sub-columns grouped to form a plurality of sub-divided main columns, a manually operable means for rotating said rotatable means past said Window, an index glass slidable along said Window and bearing sub-dividing lines corresponding to the sub-divisions of said main column, and computing mechanism in said casing and co-related With said rotatable means for combining selected values of said functions into a value designating a solution of a navigational problem, said computing mechanism having operating members bearing indicia corresponding to said selected values.

13. In apparatus of the class described, the combination. in a single instrument of a casing having a Window therein. a rotatable means in said casing embodying in tabulated form values of a plurality of functions necessary to a. solution of navigational problems, the individual functions being arranged in sub-columns grouped to form a plurality of sub-divided main columns, a manually operable means for rotating said rotatable means past said Window, an index glass slidable along said Window and bearing sub-dividing lines corresponding to the sub-divisions of said main column, indiciaon said casing to indicate delimiting values of each main column, and computing mechanism in said casing and cpo-related With said rotatable means for combining selected values of said functions into a value designating a solution of a navigational problem, said computing mechanism having operating members bearing indicia corresponding to said selected values.

14. In apparatus of the class described, the combination in a single instrument of a casing having a window therein, a rotatable means in said casing embodying in tabulated form values of functions necessary to a solution of navigational problems, a rotatable operating knob, operative connections between said knob and rotatable means and effective in only one direction of rotation of said knob to rotate said means past said Window, an index slidable along said Window for selecting values appearing therein, and computing mechanism in said casing and corelated with said rotatable means for combining indexed values of said functions, said computing mechanism being capable of registering and computing functions tabulated in said rotatable means.

15. In apparatus of the class described, the combination in a single instrument of a casing having a Window therein, a rotatable means in said casing embodying in tabulated form values of functions necessary to a solution of navigational problems, a rotatable operating knob, operative connections between said knob and rotatable means and eective in only one direction of rotation of said knob to rotate said means past said Window, said connections including means for reversing the direction of rotation of said rotatable means, an index glass slidable along said window for selecting values of said functions appearing therein, and computing mechanism in said casing, and co-related With said rotatable means for combining indexed values, said computing mechanism being-capable of registering and computing functions tabulated in said rotatable means.

16. A navigational instrument comprising in combination a casing having a Window therein, means mounted in said casing for movement past said Window and embodying values of functions necessary to a solution of an astronomical triangle, a manually operable member for moving said means, an index means slidable along said window to select desired values appearing therein, means on said casing for indicating steps to be performed to obtain the desired solution, and computing mechanism in said casing and corelated with said first named means for combining indexed values in accordance With steps indicated by said indicating means, said computing mechanism bearing 1ndic1a corresponding to the values of functions selected from said first named means.

17. -In apparatus of the class described,

` the combination of a casing having a window therein, a pair of rollers mounted in said casin a table mounted on said rollers and movab e past said Window, said table bearing in tabulated form values of functions necessary to a solution of navigational problems, a driving gear for each of said rollers, an axially displaceable operating gear adapted in different positions to selectively engage said driving gears, means for locking said operating gear in a selected position, an index for selecting tabular values appearing in'said window, and computing mechanism in said casing and co-related with said table p for combining indexed values, said computing mechanism bearing idicia corresponding to values appearing in said table.

18. Apparatus of the class described comprising in combination a casing having a pair of Windows therein, a plurality of means movably mounted in said casing for movement past said Window and each embodying values of functions necessary to a solution of navigational problems, manually operable means for moving each of said first named means independently, index means for each of said Windows for delimiting and selecting a desired value appearing therein, means on said casing to indicate the steps to be performed in combining indexed values into a value designating a desired solution, and computing mechanism in said casing for combining indexed values, said computing mechanism having operating members bearing indicia corresponding to values selected from said plurality of means.

19. Apparatus for the solution of navigational problems comprising the combination in a unitary self-contained instrument of means embodying tables of functions of an astronomical triangle including numerical functions and functions tabulated in angular measure, index means for selecting desired values fromv said tables, means for presenting said tabulated values in succession to said index means, and mechanical adding and subtracting means, said tables comprising values precomputed and combined into 'functions necessary for the desired solution by said mechanical means and said mechanical means having operatingY members corresponding to values selected from said tables and being capable of registering both numerical functions and functions in angular measure.

20. Apparatus for the solution of navigational problems comprising the combination in a unitary self-contained instrument of means embodying Itables of functions of an astronomical triangle including numerical functions and functions tabulated in angular measure, index means for selecting desired values from said tables, means for presenting said tabulated values in succession to said index means, and mechanic-al adding and subtracting means, said tables comprising values precomputed into functions necessary for the desired solution by said mechanical means and said mechanical means having operating members corresponding to values selected from said tables and being capable of registering both numerical functions and functions in angular measure, said mechanical means including means for making a printed record of the desired solution and a plurality of designating keysfor printing on said record designations required in said solution.

In testimony whereof I have hereunto set my hand at the city of Washington, District of Columbia, this sixth day of June 1930.

ROBERT E. JASPERSON. 

